Digital images often contain unwanted noise that can degrade the quality of the image. Researchers have experimented with a substantial number of model/algorithm combinations in an attempt to find combinations that can effectively remove the noise from the images while being computationally efficient. What follows is a brief description of some of the example models and algorithms that have been employed thus far in removing noise from images.
Active Appearance Models are iterative algorithms driven by data and a Principal Component Analysis-like model to find objects of interest in the image. The solution depends on the starting location, so these models are usually used in cooperation with other algorithms or with user initialization. A more complete solution for object or shape detection is offered by the Shape Regression Machine, where an image based regression algorithm is trained to find a vector toward the object of interest from any random location inside the image. Fast and robust object detection is obtained by using hundreds of random initializations and a verification step based on Adaptive Boosting. The Shape Regression Machine can thus be seen as a trained model−algorithm combination for object or shape detection.
Energy based models have also been evaluated for noise removal methods. These models are trained in such a way that the minimum energy is at the desired location on the training set, independent of the optimization (inference) algorithm that is used, and therefore, specific conditions on the energy function are imposed. Other model−algorithm combinations exist where the model can be learned without imposing any computational complexity constraints. One combination in this category is a Conditional Random Fields (CRF), which is based on pair-wise potentials trained for object classification using boosting and a pixel-wise loss function. Each classifier is based on features from the data and on recursive probability map information. Such methods train Markov Random Field (MRF) model−algorithm combinations that slowly decrease in speed at each training iteration, because the models become more and more complex.
A loss function can be used to evaluate and train model/algorithm combinations; however, previous methods using the loss function employ computationally intensive inference algorithms that are focused on exact Maximum A Posteriori (MAP) estimation for obtaining a strong MRF optimum.
Many real-world digital imaging or computer vision problems can be regarded as graph-based optimization problems, where the pixels are smaller granularities of the image. In some systems employing graph-based optimization (e.g. material science), there exists a unique energy function that can be described mathematically and can accurately represent the relationship between the graph nodes. In image analysis, however, there is usually no known mathematical model that is computationally feasible and can accurately represent the underlying phenomenon. Nevertheless, one can typically find measures to quantitatively evaluate the performance of any algorithm that attempts to solve the graph-based optimization problem. In general, these problems are solved by constructing a model as an energy function such that the task goal is a minimum of this function, and by employing a graph-based optimization algorithm to find this minimum. This approach faces at least the following two challenges. First, the energy function should be computationally feasible in the sense that the minimum should be found in polynomial time. This does not usually happen in reality, since finding the global minimum for many energy functions associated with real-world applications is nondeterministic polynomial-time hard (NP hard) therefore polynomial-time algorithms are not expected to be found.